3.1 Introduction

In Chap. 2 we described qualitatively various phenomena that are responsible for the flow of current in MOS transistors. A quantitative description of such phenomena using semiconductor physics concepts leads to quantitative models for the current in the device as a function of the externally applied bias voltages. The process of deriving such models of adequate accuracy can take a large number of pages and is the subject of other books [ ^{[1] [2] [3] [4]}]. Here we will present the results of such extensive derivations, and we will concentrate on their interpretation and correct use.

Our emphasis will be on simple models, appropriate for hand calculations and for fast computer simulations. We will present such simple models for each of the weak inversion and strong inversion regions. We will then show how, through interpolation, one can construct models that are valid in all regions (including moderate inversion) without excessive complexity. We will also consider a number of improvements that can be made, in order to extend the validity of the models in the presence of nonconstant mobility, temperature variations, and effects that appear when the device dimensions are made very small. We will conclude the chapter with a discussion of the present state of computer-aided design (CAD) models and of the procedures through which values are chosen for the model parameters.

We will assume that the devices considered are nMOS, unless stated otherwise. All voltages will be assumed to be dc in this chapter,...